Problem: $5kl - km - 8k + 1 = 4l - 1$ Solve for $k$.
Solution: Combine constant terms on the right. $5kl - km - 8k + {1} = 4l - {1}$ $5kl - km - 8k = 4l - {2}$ Notice that all the terms on the left-hand side of the equation have $k$ in them. $5{k}l - 1{k}m - 8{k} = 4l - 2$ Factor out the $k$ ${k} \cdot \left( 5l - m - 8 \right) = 4l - 2$ Isolate the $k$ $k \cdot \left( {5l - m - 8} \right) = 4l - 2$ $k = \dfrac{ 4l - 2 }{ {5l - m - 8} }$ We can simplify this by multiplying the top and bottom by $-1$. $k= \dfrac{-4l + 2}{-5l + m + 8}$